Transformation of probability distribution into fuzzy set interpretable with likelihood view

Recent research agrees on the utility of fuzzy reasoning for the development of Decision Support Systems, which help to classify clinical data. In this context, methods or techniques for representing fuzzy terms in the form of interpretable fuzzy sets obtained from numerical data are strongly required. Typically, in medical settings, statistical data are available or can be obtained from rough data, in the form of probability distributions or likelihood functions. Until now, no theoretical approach was proposed for transforming a probability distribution into a likelihood view fuzzy set. In this paper, a method is developed which generalizes some existing approaches by giving them a theoretical justification. The method enables the construction of normal fuzzy sets, which can be chosen to have a triangular or trapezoidal shape where lateral edges are adapted depending on the input probability distribution. The method was assessed through its application to a simulated normal probability distribution and to real case study pertaining the classification of Multiple Sclerosis lesions.